The end points in the dispersion of Holstein polarons

Abstract

We investigate the existence of end points in the dispersion of Holstein polarons in various dimensions, using the Momentum Average approximation which has proved to be very accurate for this model. An end point separates momenta for which the lowest-energy state is a discrete level, i.e., an infinitely-lived polaron, from those where the lowest-energy feature is a continuum in which the "polaron'" is signalled by a resonance with a finite lifetime. While such end points are known to not appear in 1D, we show here that they are generic in 3D if the particle-boson coupling is not too strong. The 2D case is "critical": a pure 2D Holstein model has no end points, like the 1D case. However, any amount of interlayer hopping leads to 3D-like behavior. As a result, such end points are expected to appear in the spectra of layered, quasi-2D systems described by Holstein models. Generalizations to other models are also briefly discussed.

6 pages, 6 figures

References in corpus (7)

• Green's function of a dressed particle
• The Green's Function of the Holstein Polaron
• Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron
• Distribution of Localized States from Fine Analysis of Electron Spin Resonance Spectra in Organic Transistors
• Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
• Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass
• Holstein polaron in the presence of disorder

Cited by in corpus (2)

• Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO${}_3$
• Adiabatic theory of the polaron spectral function